1. Field of the Invention
The present invention relates to interferometric and dispersive spectroscopy of broadband waves such as light, and more specifically the interferometric measurement of effects which can be made to produce phase shifts such as Doppler velocities, distances and angles, and furthermore the mapping of spectra.
2. Description of Related Art
Spectroscopy is the art of measuring the wavelength or frequency characteristics. There are two complementary forms of spectroscopy method currently used today. In the oldest form, a prism or grating disperses input illumination (let us call it light) into independent channels organized by wavelength or frequency. A spectrum is created which is the intensity versus wavelength channel. This is a scalar versus wavelength channel. In the other method, called Fourier transform spectroscopy, an interferometer having a variable path length difference (called the delay) interferes the illumination with a delayed copy of itself, creating an interferogram. The Fourier transform of this yields the spectrum. Previously, the two methods have not been used together where the interferometry and dispersiveness have had equal emphasis.
An important practical use of spectroscopy is the measurement of Doppler shifts. In addition to many industrial applications of Doppler velocimetry, astronomers measure the Doppler velocity of stars in order to deduce the presence of planets orbiting around the star. The stellar spectrum contains numerous dark absorption lines against a bright continuum background. These spectral lines are randomly distributed about 1 Angstrom apart from each other. A slight change in the average position of these lines is the Doppler effect to be measured. The average width of these stellar lines is about 0.12 Angstroms in the visible, which corresponds to an equivalent Doppler velocity width of about 6000 m/s. Hence, measuring Doppler velocities below 6000 m/s is extremely challenging and requires carefully dividing out the intrinsic behavior of the instrument from the raw data.
A 1 m/s velocity resolution is desired in order to reliably detect the presence of Jupiter and Saturn-like planets, which produce 12 m/s and 3 m/s changes respectively in the stars intrinsic velocity. Current astronomical spectrometers are based on the diffraction grating. These have a best velocity resolution of 3 m/s, but is often 10 m/s in practice. This resolution is insufficient to reliably detect Saturn-like extrasolar planets. This limit is related to the difficulty in controlling or calibrating the point spread function (PSF).
The PSF is the shape of the spectrum for a perfectly monochromatic input. Ideally this is a narrow peak of well-determined shape. Unfortunately, the PSF of actual gratings varies significantly and in a complicated way against many parameters such as temperature, time, and average position in the spectrum. It is a complicated function that requires many mathematical terms to adequately approximate it. This is fundamentally due to the hundreds or thousands of degrees of freedom of the diffraction gratingxe2x80x94at least one degree of freedom per groove of the grating. These degrees of freedom must be carefully calibrated, otherwise drifts can cause apparent Doppler velocities much larger than the effect being sought. The calibration process is time consuming.
Another disadvantage of conventional astronomical spectrometers is their large size, which can be several meters in length. Large distances between optical components, which need to be held to optical tolerances, require very heavy and expensive mounts and platforms to prevent flexure. This dramatically increases expense and prevents portability. Practical use aboard spacecraft or aircraft is prevented. The high expense limits the number of spectrometers which can be built to a few, only by well-endowed institutions.
Other disadvantages include a very limited field of view, which is called etendue and is the area of the input beam times its solid angle. This is due to the narrowness of the slit at the instrument entrance that defines the range of entry angles. In a grating or prism based instrument the entry angle and the wavelength, and hence deduced Doppler velocity, are directly linked. The slit needs to be narrow to provide better than 0.05 Angstrom resolution to resolve the stellar spectral lines. Atmospheric turbulence causes the star image to dance around, sometimes off the slit opening. This reduces the effective instrument throughput. Furthermore, changes in intensity profile across the slit have to be carefully deconvolved from the data, since the Doppler velocity gradient across the slit is approximately 3000 m/s. Thus achieving 3 m/s velocity accuracy is extremely difficult with a dispersive spectrometer, and 1 m/s has never been achieved.
An interferometer is attractive for spectroscopy because its angular dependence can be made very small or zero. This allows wider slits, and hence accommodating blurrier star images at high throughput, for the same equivalent spectral resolution. Secondly, its PSF is a sinusoid, which is a simple mathematical function having only 3 degrees of freedom (phase, amplitude and intensity offset). This makes calibration of instrument and processing of data fast, since standard vector mathematics can be used. Secondly, this makes it easy to reject noise not having the expected sinusoidal shape. Furthermore, the spectral resolution can be made almost arbitrarily large simply by increasing the delay (difference in path length between the two interferometer arms). The interferometer is compact and inexpensive, because the optical components need only be a few millimeters or centimeters from each other.
The important difficulty of an interferometer measuring broadband illumination is poor fringe visibility. Fringe phases naturally changes with wavelength. When component fringes of many wavelengths combine on the same detector, they reduce the visibility of the net fringe. For this reason conventional interferometer based instruments such as Fourier transform spectrometers without any wavelength restricting filters are rarely used in low light applications.
A solution to this problem is to combine a wavelength disperser with the interferometer so that fringes of different wavelengths do not fall on the same place on the detector. The combination of disperser and Fabry-Perot interferometer is described in the book xe2x80x9cPrinciples of Opticsxe2x80x9d by Max Born and Emil Wolf, Pergamon Press, 6th edition, on page 336, section 7.6.4 and their FIGS. 7.63, 7.66 and references therein. Distinctions exist between apparatus described in xe2x80x9cPrinciples of Opticsxe2x80x9d and the present invention. The Born and Wolf device produces fringes that are narrow and peak-like, not sinusoidal. Consequently, the fringe shape is not described by a 2-element vector. This reduces accuracy when trying to measure small phase shifts. Furthermore, phase stepping is not involved. Thirdly, a heterodyning action is not employed to shift high-resolution spectral details to low spectral resolution.
In some kinds of metrology a secondary effect, such as temperature, pressure or acceleration, is measured by the change it induces in the delay of an interferometer, such as through changing the position of a reflective surface or altering a refractive index. The delay is then sensed by the phase of a fringe. In current devices monochromatic illumination, such as laser illumination, is needed to produce visible fringes from non-zero delays. (The delays are often non-zero for practical reasons, or to have a significant range of travel.) However, the use of monochromatic illumination creates fringe skip ambiguities which make the absolute size of the effect being measured ambiguous. Only small changes can be reliably measured. Broadband light solves the fringe skip problem, but produces insufficient fringe visibility because its coherence length (about 1 micron) is usually very much shorter than the delay.
In a related metrology, fringe shifts can be used to measure angles of distant objects such as stars. Light from the star is collected at two separate places a baseline distance apart, and interfered against each other at a beamsplitter. This is called long baseline interferometry. Effectively, an interferometer is created in the triangle consisting of the target and the two collecting ports. In the case of broadband targets such as starlight, the short coherence length of the illumination (about 1 micron) restricts the interferometer delay to be very near zero in order to produce visible fringes. This restricts the angular range. Secondly, an interferometer""s phase is sensitive to the illumination""s spectral character on bandwidth scales given by 1/(delay). Having a small or zero delay means the interferometer phase is sensitive to the overall shape of the illumination spectrum, and this can vary erratically due to atmospheric turbulence. More accuracy could result if the interferometer were only sensitive to behavior on short bandwidth scales, such as 1 Angstrom, because this is less affected by the atmosphere. This would require using large delays (several millimeters at least), which can""t be done with the present long baseline interferometers.
A related spectroscopic long-baseline interferometer technique is described by Kandpal et. al., in Journal of Modern Optics, vol. 42, p447-454 (1995). Intensity modulations are observed in a spectrometer which are due to the angular separation of two stars. However, this technique does not use heterodyning, nor phase stepping nor slit fringes, nor an iodine cell, nor use vectors to describe the data at each wavelength channel. Because of this, the typical maximum angle it can measure is 8000 times smaller than what my invention can measure.
It is an object of the invention to measure the spectral characteristics of waves, especially broadband waves. These waves include electromagnetic waves, and any other waves that can be passed through an interferometer where they interfere with a delayed copy of themselves, and can be dispersed into intensity-detecting channels organized by frequency or wavelength. The dispersion can be either before or after the interference. Broadbandedness could be defined as when, with the interferometer were used by itself without the disperser, the phases of the fringes of different spectral regions within the input illumination are more than 90 degrees different from each other, and thereby start to diminish the net fringe visibility.
The invention comprises the series combination of a disperser which organizes the waves by frequency or wavelength, and the interference of the waves with a delayed copy of themselves. It is an object of the invention to create a spectrum which has fringes whose phase and amplitude can be determined for a given wavelength channel independent of information from other wavelength channels. Such a spectrum is called a fringing spectrum. To determine fringe phase and amplitude of a given wavelength channel independent of other channels, the interferometer delay is arranged to vary, either spatially along the slit of the disperser (which is perpendicular to the dispersion axis), or temporally by xe2x80x9cphase steppingxe2x80x9d, which is to take repeated exposures while changing the overall interferometer delay for all channels. When the delay changes along the slit, such as by tilting an interferometer mirror or beamsplitter, fringes are created which cause the intensity profile along the slit to vary sinusoidally with a finite period.
Regardless of any fringing behavior along the slit direction, an interferometer always has sinusoidal behavior versus frequency. This is called the xe2x80x9cspectral combxe2x80x9d. This comb may not be resolved by the disperser, but its presence is still key in producing Moire fringes.
The effect of passing light through both the interferometer and disperser is to multiply the spectral comb with the illumination spectrum. Together with the presence of blurring along the dispersion axis, a heterodyning effect occurs which creates Moire fringes. These shift high spectral resolution details to low spectral resolution. Hence, a low spectral resolution disperser can be used, even though high spectral resolution information is being sensed. This lower costs, increases throughput and increases field of view compared to a high-resolution disperser used alone.
It is an object of the invention to express the fringing spectrum as a 2-dimensional vector versus wavelength or frequency channel, which is called a vector spectrum. This data format is also called a xe2x80x9cwhirlxe2x80x9d. The length and angle of the vector when expressed in polar coordinates represent the fringe amplitude and phase, respectively. The vectors can be computed by evaluating the Fourier sine and cosine amplitudes, for a periodicity near the natural fringe periodicity along the slit axis, and assigning these to the X and Y rectangular coordinates of the vector. In the case of infinite fringe periodicity along the slit, the Fourier components cannot be determined from a single exposure, but can be determined if the several exposures are made while incrementing the interferometer by a small amount, such as equivalent to a quarter wave, and knowing that the fringes will shift in phase proportional to the delay change. This technique is called phase stepping. Phase stepping is recommended even for finite fringe periodicity along the slit, because it assists in distinguishing true fringes from common-mode noise.
The embodiment of the invention having a single approximately fixed interferometer delay can measure broadband phase shifts due to the Doppler effect of a moving source. Due to the action of the disperser, the optimum delay value is approximately half the coherence length (xcex2/xe2x80xa2xcex) of the illumination that is due to the spectral lines or other narrow features, not the short coherence length due to the continuum background. That is, xe2x80xa2xcex is given by the 0.12 Angstrom width of the spectral line instead of hundreds of Angstroms of the continuum. In the absence of a disperser the relevant coherence length would be due to the broad continuum background, and therefore thousands of times shorter.
This delay choice provides a good tradeoff between fringe visibility and phase shift per velocity ratio. For starlight this is a delay of about 11 mm.
The Doppler velocity is proportional to the whirl rotation. This can be found by taking the dot product of the input whirl against an earlier measured whirl, and against the earlier measured whirl rotated by 90 degrees. The whirl dot products are generalized dot products evaluated by summing or averaging the channel dot product over all wavelength channels. The dot product is called xe2x80x9cgeneralizedxe2x80x9d because it sums products over both the spatial and wavelength indices. The subsequent arctangent of the two aforementioned dot products yields the whirl angle. Note that a key advantage implicit in the generalized dot product is that the summation over wavelength channels happens prior to applying the arctangent function. This prevents large discontinuities in the arctangent function that would occur for spectral channels that have zero or small fringe visibility.
Since the whirl rotation is dependent on both the interferometer delay and the illumination spectrum, measuring a Doppler effect requires independently determining the interferometer delay, which could be wandering due to vibration and thermal drift. This can be accomplished by including a reference spectrum with the target illumination, such as by passing the light through an iodine vapor cell which imprints its own absorption lines, which have stable positions unrelated to the Doppler effect. This creates a net whirl which contains two components, corresponding to the target illumination and the reference spectrum. The difference in rotation between the target whirl and the reference whirl components yields the target Doppler velocity. The rotational positions of the target and reference whirl components can be found by expressing the total whirl as a linear combination of component whirls with unknown coefficients, and applying generalized dot products.
The advantage of this invention is an instrument which is much more compact, lower cost, and having a greater field of view than a conventional dispersive spectrometer of 0.05 Angstrom, and has much greater signal to noise ratio than an interferometer used alone.
Another embodiment of the invention uses the interferometer delay as a means of measuring secondary effects such as temperature, pressure and acceleration. These effects are arranged to change the delay in a known manner, such as by moving a reflective part of the interferometer cavity or altering the refractive index of the cavity medium. A steady reference spectrum is used for the illumination. Then changes in the whirl rotation can be ascribed to changes in the interferometer delay and hence the secondary effect. Since the interferometer delay may already be changing due to deliberate phase stepping, it is advantageous to include a second interferometer in series with the probe interferometer cavity to act as a reference cavity. Then the change of one interferometer delay compared to the other provides the measurement of the secondary effect being probed. This method differs from conventional interferometric measurements of cavity lengths by the use of broadband instead of monochromatic illumination. This allows a unique determination of the absolute cavity length without the fringe-skip ambiguity of monochromatic waves.
A variation of this method can measure the angular position of distant objects such as stars if the interferometer cavity is replaced by a long baseline interferometer, which collects starlight at two separate places a baseline apart from each other and interferes them. Effectively, the triangle consisting of the star and the two collection ports forms the interferometer cavity. Changes in star angle cause an arrival time difference in the starlight interfering with itself. This creates a rotation of the whirl which is measured. The target light can be passed through an iodine vapor absorption cell to imprint a known spectrum. This way, the star""s velocity will not affect the measurement because the stellar spectrum can be ignored, and targets having no intrinsic spectral lines or narrow features can be used. Furthermore, greater angular separations can be measured because the iodine linewidths are much narrower (by a factor 8) than stellar linewidths, so proportionately greater arrival time differences at the beamsplitter can be measured. By observing two or three stars simultaneously through the use of beamsplitters at the collection ports, poorly known instrumental parameters such as the baseline length and the phase stepping amount can be determined from the data. The advantage of using this technique is that more precise phase shifts can be measured than in conventional long baseline interferometry, over larger angular range, because the imprinted iodine spectrum is much more information rich than the star""s intrinsic spectrum.
Furthermore, the 2-d vector format of the whirl preserves the polarity of the Moire fringes, which preserves polarity of arrival time difference and hence the target angle relative to the baseline. This is not possible with devices that only record the intensity (scalar) spectrum.
Measuring a Doppler shift of a spectrum is a different task than mapping a spectrum, which is the purpose of many conventional spectrometers. The former task requires only a subset of the full spectral information. An embodiment of the invention which modifies the interferometer to have several parallel channels of different delay striking separate positions of the detector can indeed map a spectrum. Each interferometer delay produces a whirl which is responsible for measuring a particular subset of the full spectral information. The interferometer delays are chosen to be different from each other so that the set of them samples all the desired spectral information. The separate spectral information is combined together mathematically, using the knowledge that the Moire fringes of the fringing spectrum manifest a heterodyning process that beats high spectral detail to low spectral detail. The reverse process is employed to mathematically reconstruct the full spectrum of the input illumination. This process involves Fourier transforming each whirl from frequency-space to delay-space, translating each in delay-space by the specific interferometer delay used, concatenating all these together, then inverse Fourier transforming to yield a net spectrum. The advantage of this invention for mapping a spectrum is that it forms a more compact, lower cost device than dispersive spectrometers for the same equivalent spectral resolution. And compared to conventional Fourier transform spectrometers it can measure single shot events (instantaneous measurement) because it does not require waiting for an interferometer delay to be scanned. The delays are fixed. The lack of significant moving parts is also an advantage for space-based operation.